The present invention relates to semiconductor process flow disposition optimization, and more particularly, to techniques for semiconductor process flow disposition optimization using clamped Monte Carlo distribution.
Determining the critical parameters which dominate the characteristic outcome distribution (e.g., pitch walk control) of a complex multi-step semiconductor process flow such as Self-Aligned Quadruple Patterning (SAQP) are quite difficult. Typically, engineers will run a variety of experimental binary splits to understand the process. Binary splitting is a technique for numerical evaluation of series with rational terms. These binary splitting techniques are, however, time consuming and expensive for most applications.
Further, use of a binary splitting approach may or may not capture the complete process statistical view and understanding of the combinatorial nature of all the process interactions. Additionally, the tradeoff between the variance control of the disposition process and the variance of the outcome critical parameter are often poorly understood.
Accordingly, improved techniques for process flow disposition optimization would be desirable.
The present invention provides techniques for semiconductor process flow disposition optimization using clamped Monte Carlo distribution. In one aspect of the invention, a method for optimizing a semiconductor fabrication process is provided. The method includes: providing a model of the fabrication process; identifying sensitive parameters of the fabrication process using Monte Carlo simulations that sample sections of experimental parameter populations from the fabrication process as input to the model to determine parameters which impact an outcome of the Monte Carlo simulations, wherein the parameters which impact the outcome of the Monte Carlo simulations are the sensitive parameters; bounding the experimental parameter populations of the sensitive parameters to improve the outcome of the Monte Carlo simulations; and modifying the fabrication process based on the providing, identifying and bounding steps to improve an output of the fabrication process.
A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings.
As provided above, the use of conventional approaches such as binary splitting to determine which parameters dominate the characteristic outcome distribution of a complex multi-step semiconductor process flow are typically time consuming and expensive, and oftentimes do not provide a comprehensive insight into the nature of all of the process interactions involved. Advantageously, provided herein are techniques for quantitatively determining the process sensitivity of a given step in a complex multistep process that controls the downstream process critical dimension (CD) structural stack parameter such as Self-Aligned (or Spacer-Assisted) Quadruple Patterning (SAQP) pitch walk control. Namely, as will be described in detail below, the present techniques identify what the key sensitive parameters are, and what the relative contribution of these key sensitive parameters are to CD outcome.
For instance, using the identified sensitive parameters, a determination is made of the expected variance improvement of a downstream process CD structural stack parameter as a function of restricting or clamping the variance (i.e., restricting the variance to a given range) of the key sensitive parameters. This disposition technique can be applied, either as a standard process disposition or after regression-based predictive models highlight the need for substantial corrective action.
The present techniques are now described by way of reference to methodology 100 of
The goal is to be able to identify the parameters in a multi-step process that affect the outcome downstream, and by how much, in order to know what upstream parameters to control in order to achieve a desired downstream outcome. For instance, SAQP is a tightly-coupled, multi-step process, where what happens in one step might depend on what happens in one or more upstream steps, and so on. These dependencies are, however, not always apparent, and it is the goal of the present techniques to identify sensitivities among parameters to enable a user to know what parameters to control in order to affect a downstream outcome, and by how much. Using SAQP as an example, as will be described in detail below, this process involves the deposition, patterning, etc. of multiple materials in a variety of different steps. It may not always be apparent what impact, if any, a certain parameter (such as the thickness of a given spacer) has on what downstream outcome, and what is the magnitude of that impact. By way of the present techniques, a user can determine which of the multi parameters of the SAQP process to tune in order to achieve a desired downstream outcome.
As highlighted above, according to an exemplary embodiment the present techniques employ Monte Carlo methods which are based on probability distributions extracted from experimental parameter data. As is known in the art, a Monte Carlo method is a statistical technique for modelling stochastic systems to determine the probable outcomes from the system based on random inputs. The Monte Carlo method can be used to model systems involving complex interactions of many variables.
For illustrative purposes only, semiconductor fabrication process examples will be referenced in the description of methodology 100. For instance, one such process is SAQP. SAQP is a process that can be employed to pattern features at pitches smaller than achievable using direct patterning. Namely, SAQP enables the patterning of wider features, followed by two successive cycles of spacer deposition (i.e., Spacer 1 and Spacer 2), spacer etch, and core removal.
Referring briefly to
While SAQP allows patterning at sub-lithographic pitches, it also involves more process steps, more complex interactions of the associated lithography and etching processes, and hence more chances for variation. One such process variation is pitch walking (PW). Pitch walking occurs when the lithography, material deposition and/or etching process involved in SAQP generates a repeating, non-uniform grating of space and line critical dimensions. While an SAQP is a good example to use to illustrate methodology 100, it is to be understood that the present techniques are more broadly applicable to any stochastic process including, but not limited to, processes involved in semiconductor fabrication.
As shown in
In step 102, the fabrication process is modeled. According to an exemplary embodiment, an analytical model is employed having equations that describe downstream outcome critical dimensions (CD) based on upstream input parameters. For instance, by way of example only, a set of analytical equations can be employed for evaluating the outcome CD of an SAQP process based on input parameters such as the thicknesses of Spacer 1 and Spacer 2 (TSP1 and TSP2), mandrel CD and pitch (CDMandrel and PitchMandrel), etc. For example,
CD
Fin
=T
SP2 (1)
CD
FinTrench
=T
SP1 (2)
CD
Trench1
=CD
Mandrel−2*(TSP2) (3)
CD
Trench2=PitchMandrel−CDMandrel−2*(TSP1)−2*(TSP2) (4)
wherein Fin Trench refers to the trench between fins from the same Spacer 1, Trench 1 refers to the trench between fins from adjacent Spacers 1, and Trench 2 refers to the trench between fins from adjacent mandrels.
To use a simple example, referring to Equation 1, the critical dimension of the fins patterned in the substrate via the Spacers 2, i.e., CDFin, is equivalent to the thickness of Spacer 2, i.e., TSP2. Thus, the model is based on structural wafer stack geometries (e.g., space width=pitch−width of structure) that describe a single step or multiple steps of the fabrication process.
Further, the equations which describe tightly-coupled, multi-step processes can be analytically coupled. For instance, again using Equations 1-4 above as an example, the outcome CD of the trench gap CDTrench2 is dependent on a combination of parameters, e.g., PitchMandrel, CDMandrel, TSP1 and TSP2. See, e.g., Equation 4. It is noted that these analytical equations for an SAQP process are only being used herein as an illustrative example. The present techniques are broadly applicable to any stochastic fabrication process and can be implemented using a variety of different models as would be apparent to one skilled in the art.
As will be described in detail below, simulations will be run with the model using actual experimental data to determine probable outcomes. Thus, metrology data is needed for extracting these experimental values of the relevant geometrical quantities from the fabrication process that are used for the experimental parameter values of the analytic equations in the model (e.g., N sets of experimental parameter values would be needed for the n steps of a complex, multi-step fabrication process). By way of non-limiting example only, a scatterometry-based metrology is suitable for extracting this experimental parameter data. Scatterometry is a non-destructive method to assess detailed structural requirements.
In step 104, Monte Carlo simulations are performed based on probability distributions extracted from experimental parameter data being used as input to the model (from step 102) to: i) identify sensitive parameters, i.e., those parameters of the fabrication process which impact the outcome of the simulations (for example, identify which parameters, if varied, impact (i.e., reduce) pitch walking variance in the simulations), and ii) determine the relative contribution these identified sensitive parameters have to that outcome. See step 106, described below. The terms “upstream” and “downstream” are used herein to describe the relative order of steps/outcomes in a fabrication process flow. For instance, in an SAQP process flow, mandrel formation occurs upstream from spacer formation, and trench patterning using the spacers is downstream from the mandrel and spacer formation, and so on.
As provided above, Monte Carlo simulations are used to determine the probable outcomes from a stochastic system. The Monte Carlo simulations in the present process are based on experimental parameter data. See, for example, the histogram in
To identify the sensitive parameters, the population is restricted (for a given input parameter such as critical dimension (CD) width), e.g., to μ+kσ(k=2,3), wherein μ is the mean, in the present example (see
The sensitive parameters are identified by assessing the impact this restriction (sampling) has on the outcome simulation population distribution which is representative of the impact the sensitive parameters have on the outcome of the process. See, for example,
Those parameters that have an impact on the simulation population distribution (such as those modeled in
To further illustrate the sensitivity analysis performed in step 104, reference is now made to exemplary methodology 600 of
As provided above, the Monte Carlo simulation is performed on a restricted (or ‘clamped’) population of the experimental parameter data. Thus, in step 604 the population for the single input parameter selected in step 106 is limited to μ+kσ{where k=(−4,−3), (−3,−2) . . . (3,4)}, wherein μ is the mean. This process for limiting the Monte Carlo population is further illustrated in
The Monte Carlo simulation is performed using that restricted (sampled) population (i.e., the Monte Carlo population) as input to the model, and in step 606 the shift of the mean μ for the simulation population distribution with respect to the experimental population distribution is measured to determine an impact the restriction of the Monte Carlo population has on the outcome (e.g., in a SAQP process where output variation is an indicator of pitch walking variance). For each parameter, the notion is that the larger the mean shift, the greater the sensitivity of the parameter. Further, the present techniques serve to normalize all of the parameters as a function of kσ thereby allowing one to evaluate (i.e., rank) different parameters at the same scale.
See, for example, the outcome distributions in
In step 606, another section of the population is sampled with another selection from k=(−4,−3),(−3,−2) . . . (3,4), and a Monte Carlo simulation is run on that sampled (Monte Carlo population). For instance, if in step 604 μ+kσ(k =−4,−3), then in step 606 μ+kσ(k=−3,−2), and so on. Steps 604 and 606 are then repeated until all of sections μ+kσwhere k={(−4,−3), (−3,−2) . . . (3,4)} have been sampled.
See, for example,
Once all of sections μ+kσ{where k=(−4,−3) ,(−3,−2) . . . (3,4)} for the given input parameter have been sampled, in step 608 another input parameter is selected. As shown in
See, for example,
From the examples provided in
Referring back to methodology 100 of
μ+kσ{for k=(−4,4),(−3,3),(−2,2),(−1,1)}
See, for example,
Finally, in step 108 the fabrication process is modified (or suggestions can be made to modify) based on the outcome from steps 102-106 with the goal being to improve the output (e.g., reduce pitch walk variation in the output) thereby optimizing the fabrication process. For instance, as described above, the sensitive parameters of the process (e.g., CDMandrel, TSpacer1, etc. for the exemplary SAQP process) have now been identified using actual experimental parameter data, as well as the relative impact these sensitive parameters have on the outcome (e.g., CDMandrel variance has a greater impact on pitch walk variance than does TSpacer1).
The impact of bounding the Monte Carlo population (e.g., by cut the edges of the distribution) of these sensitive parameters has on improving the output has also now been determined. This bounding process can be applied directly to the actual fabrication process. For instance, during fabrication measurements of the sensitive parameters are made. Based on the measurements, those outlying samples with sensitive parameter values that were cut from the edges of the population distribution are either discarded or re-worked/fixed such that only those samples within specifications are carried forward. Advantageously, based on the present techniques, these determinations can be made early on in the process to avoid costly and time-consuming downstream steps being performed on non-conforming samples.
For instance, using the above SAQP example, the Monte Carlo population for CDMandrel was bounded by μ+kσ(k=−3,3). Thus, during fabrication any samples having CDMandrel values that were cut from the population can be discarded/re-worked to improve the output pitch walk variance. Further, the mandrels are placed early on in the SAQP process. Thus, much effort and expense can be saved by identifying outliers early on in the process.
The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.
The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.
Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.
Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.
Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions.
These computer readable program instructions may be provided to a processor of a computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.
The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.
The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be accomplished as one step, executed concurrently, substantially concurrently, in a partially or wholly temporally overlapping manner, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.
Turning now to
Apparatus 1600 includes a computer system 1610 and removable media 1650. Computer system 1610 includes a processor device 1620, a network interface 1625, a memory 1630, a media interface 1635 and an optional display 1640. Network interface 1625 allows computer system 1610 to connect to a network, while media interface 1635 allows computer system 1610 to interact with media, such as a hard drive or removable media 1650.
Processor device 1620 can be configured to implement the methods, steps, and functions disclosed herein. The memory 1630 could be distributed or local and the processor device 1620 could be distributed or singular. The memory 1630 could be implemented as an electrical, magnetic or optical memory, or any combination of these or other types of storage devices. Moreover, the term “memory” should be construed broadly enough to encompass any information able to be read from, or written to, an address in the addressable space accessed by processor device 1620. With this definition, information on a network, accessible through network interface 1625, is still within memory 1630 because the processor device 1620 can retrieve the information from the network. It should be noted that each distributed processor that makes up processor device 1620 generally contains its own addressable memory space. It should also be noted that some or all of computer system 1610 can be incorporated into an application-specific or general-use integrated circuit.
Optional display 1640 is any type of display suitable for interacting with a human user of apparatus 1600. Generally, display 1640 is a computer monitor or other similar display.
Although illustrative embodiments of the present invention have been described herein, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be made by one skilled in the art without departing from the scope of the invention.